1. Field of Invention
This invention relates to mathematical games and activities for both entertainment and skill development.
2. Prior Art
Various mathematical games (e.g., Crisswell, U.S. Pat. No. 6,581,937; Lyons, U.S. Pat. No. 5,314,190; Rheams, U.S. Pat. No. 5,338,203) have been developed with the objective of combining skill development and entertainment. Such prior art games suffer from one or more defects of the following nature: rules that are excessively involved; elements of chance that obscure the value of the desired skill development; little potential for engaging the participants at a strategic level; and limited ability to provide similar formats to accommodate both multiple participant and single participant usage.
3. Objects and Advantages
Accordingly, several objects and advantages of the present invention are consequences of overcoming those defects in the prior art. An apparatus is provided that can be utilized to create both multiple participant and single participant games. The multiple participant games utilize people's competitive spirit while single participant games, which may alternatively be called activities, provide a challenging objective. The capability of creating games or activities in a single participant format has the advantage of providing a means for the constructive and entertaining use of time in such settings as a classroom or during a long automobile ride.
Additional characteristics that overcome drawbacks in the prior art include simple rules that amount to little more than the standard rules of arithmetic operations, equal starting resources for all participants, and no chance elements other than possibly to determine order-of-play. In multiple participant games, those characteristics, together with having open display of all information, combine so as to cause participants to focus on two areas: 1) knowledge of arithmetic operation rules, and 2) the challenge of developing strategies to make better use of finite resources than their opponents. In single participant activities, the focus on knowledge of arithmetic rules remains the same, but the second focus simply shifts from making better use of finite resources, to making optimal use of those resources.
Another object and advantage arising from the family of games and activities associated with the present invention is a means by which the desired mathematical skills can be exercised in an entertaining fashion with a clear and simple objective. Since the focus is on the objective of making the best possible use of limited resources, the necessary mathematical skills are practiced in the pedagogically desirable context of a means to achieve an objective.
Another object and advantage of the present invention is a consequence of the similarity between explicitly attempting to make optimal use of limited resources in the games and activities associated with the present invention, and the implicit thinking involved in people's everyday decisions as they make trade-offs and try to do the best they can with their available resources. As a result, not only do these games and activities provide an entertaining way to practice arithmetic skills, they also provide a means to help develop explicit and rational decision making.
Yet another advantage arising from the family of games and activities associated with the present invention is that those games and activities can be scaled in size and complexity according to the capability of the participants. With elementary age children, the optimization grid size can be small, the functions simple, and the numerical values small integers. For college level use, the grid size would be larger and the maximization objective could be a challenging optimization problem.
Further objects and advantages of the present invention will become apparent from a consideration of the drawings and ensuing description.